%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO262^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:45:29 AM UTC 2026
% Result : Theorem 3.39s 2.04s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 2 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 189 ( 36 ~; 1 |; 6 &; 146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 20 ^; 18 !; 1 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(cP_decl,type,
cP: $i > $i > $o ).
thf(cE_decl,type,
cE: ( $i > $o ) > $i ).
thf(1,conjecture,
~ ( ! [A: $i] : ( cP @ A @ ( cE @ ( cP @ A ) ) )
& ! [A: $i > $i] :
~ ( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM19SK1) ).
thf(2,negated_conjecture,
~ ~ ( ! [A: $i] : ( cP @ A @ ( cE @ ( cP @ A ) ) )
& ! [A: $i > $i] :
~ ( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ! [A: $i] : ( cP @ A @ ( cE @ ( cP @ A ) ) )
& ! [A: $i > $i] :
~ ( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ! [A: $i] : ( cP @ A @ ( cE @ ( cP @ A ) ) )
& ! [A: $i > $i] :
~ ( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ! [A: $i] : ( cP @ A @ ( cE @ ( cP @ A ) ) )
& ~ ? [A: $i > $i] :
( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [B: $i > $i,A: $i] :
( ( cP @ A @ ( cE @ ( cP @ A ) ) )
& ~ ( cP
@ ( cE
@ ^ [C: $i] :
~ ( cP @ C @ ( B @ C ) ) )
@ ( B
@ ( cE
@ ^ [C: $i] :
~ ( cP @ C @ ( B @ C ) ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
! [A: $i] : ( cP @ A @ ( cE @ ( cP @ A ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(8,plain,
! [A: $i > $i] :
~ ( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(9,plain,
! [A: $i > $i] :
~ ( cP
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) )
@ ( A
@ ( cE
@ ^ [B: $i] :
~ ( cP @ B @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
! [B: $i > $i,A: $i] :
( ~ $true
| ( ( cP @ A @ ( cE @ ( cP @ A ) ) )
!= ( cP
@ ( cE
@ ^ [C: $i] :
~ ( cP @ C @ ( B @ C ) ) )
@ ( B
@ ( cE
@ ^ [C: $i] :
~ ( cP @ C @ ( B @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,9]) ).
thf(11,plain,
! [B: $i > $i,A: $i] :
( ( cP @ A @ ( cE @ ( cP @ A ) ) )
!= ( cP
@ ( cE
@ ^ [C: $i] :
~ ( cP @ C @ ( B @ C ) ) )
@ ( B
@ ( cE
@ ^ [C: $i] :
~ ( cP @ C @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
$false,
inference(pre_uni,[status(thm)],[11:[bind(A,$thf( cE @ ^ [C: $i] : ~ ( cP @ C @ ( cE @ ( cP @ C ) ) ) )),bind(B,$thf( ^ [C: $i] : ( cE @ ( cP @ C ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO262^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:42:39 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (173ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.75/1.36 % [INFO] eprover registered as external prover.
% 1.75/1.37 % [INFO] Scanning for conjecture ...
% 1.95/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.95/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.95/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.50 % [INFO] Type checking passed.
% 2.09/1.51 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.39/2.03 % [INFO] Killing All external provers ...
% 3.39/2.04 % Time passed: 1699ms (effective reasoning time: 1058ms)
% 3.39/2.04 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.39/2.04 % Axioms used in derivation (0):
% 3.39/2.04 % No. of inferences in proof: 12
% 3.39/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1699 ms resp. 1058 ms w/o parsing
% 3.39/2.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/2.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------